scholarly journals Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Monairah Alansari ◽  
Rehan Ali ◽  
Mohammad Farid
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Variational Inequality Problem ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Generalized Equilibrium Problem ◽  
Generalized Equilibrium

scholarly journals Approximation of common solutions for a fixed point problem of asymptotically nonexpansive mapping and a generalized equilibrium problem in Hilbert space

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Richard Osward ◽  
Santosh Kumar ◽  
Mengistu Goa Sangago
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Equilibrium Problem ◽  
Fixed Point Problem ◽  
Asymptotically Nonexpansive Mapping ◽  
Point Problem ◽  
Generalized Equilibrium Problem ◽  
Common Solution ◽  
Asymptotically Nonexpansive ◽  
Generalized Equilibrium

Abstract In this paper, we introduce an iterative algorithm to approximate a common solution of a generalized equilibrium problem and a fixed point problem for an asymptotically nonexpansive mapping in a real Hilbert space. We prove that the sequences generated by the iterative algorithm converge strongly to a common solution of the generalized equilibrium problem and the fixed point problem for an asymptotically nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area. Some applications of main results are also provided.

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